TESTING FOR LONG MEMORY IN VOLATILITY
研究了在波动率短记忆的零假设下，基于对数平方收益的周期图计算的长记忆参数估计量的渐近性质，并验证了GPH估计量的渐近正态性，为波动率长记忆性检验提供了Wald检验的理论基础。
We consider the asymptotic behavior of log-periodogram regression estimators of the memory parameter in long-memory stochastic volatility models, under the null hypothesis of short memory in volatility. We show that in this situation, if the periodogram is computed from the log squared returns, then the estimator is asymptotically normal, with the same asymptotic mean and variance that would hold if the series were Gaussian. In particular, for the widely used GPH estimator [d with circumflex above] GPH under the null hypothesis, the asymptotic mean of m 1/2 [d with circumflex above] GPH is zero and the asymptotic variance is π 2 /24 where m is the number of Fourier frequencies used in the regression. This justifies an ordinary Wald test for long memory in volatility based on the log periodogram of the log squared returns.